John_henderson

2 years ago

1. Given that X=x(t) and y=Y(t) are two functions of time, t and they are related by the following equations.
dx/dt - x +y=e^t
x-dy/dt=0
by eliminatiing x=x(t) and its derivative show that : d^2y/dt^2- dy/dt+y = e^t
2. Use laplace transform to solve the resulting differential eqaution :
d^2y/dt^2 - dy/dt +y = e^t
conditions y(0)=1 and dy/dt=1 and t=0
3. Hence find an explicit form of x=x(t)